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# Mathematics: Rate of Carbon Emission

The objectives of the STEM task in Mathematics lesson were to find the average rate of carbon emissions per unit of electricity (kg/kWh) and the maximum and minimum average daily carbon emissions of their household electricity bills.

The students were grouped in the same way as in the Integrated Science lesson. The lesson started a lead-in task to associate the findings of the self-made wind turbine to the real-life situation.

The power output collected in the Integrated Science lesson was used to find the number of 2W smart phones that could be charged. From the calculation, 96 self-made wind turbines made in Integrated Science were required to charge a 2W smart phone. The students thought it was unlikely to happen in real life. Thus, a 100W micro wind turbine system of Shau Kei Wan Government Secondary School was introduced to them and they were asked to calculate the number of 2W phones that could be charged by the system.

100W micro wind turbine system on the roof of the school building of Shau Kei Wan Government Secondary School

### Find the Average Rate of Carbon Emission Per Unit of Electricity Sold

From the table below, students were aware that about 70% of the electricity output was generated by burning coal, natural gas and oil. Development of sustainable energy could reduce the carbon intensity in the air. ‘Rate’ in Mathematics was a tool to help students analyse the data and interpret what the findings represent.

It was observed that students could find out the rate of carbon emissions but could not work out the average rate of carbon emissions per unit of electricity sold in 2016. After the evaluation of the effectiveness of the STEM tasks, amendments were made before the tryout lesson of the other class.

The students were asked to explain the statement ‘The rate of carbon emissions is 2kg/kWh.’ in their own words. Their work was posted on the screen for discussion. The statement was well explained by most of the groups and they showed understanding of the concept of ‘Rate’. It was found that the students could easily derive the answer of 0.54 kg/kWh, the average rate of carbon emissions per unit of electricity sold in 2016.

Carbon emissions refer to carbon dioxide emissions. Carbon dioxide is a type of greenhouse gas that contributes to climate change. According to the figures of CLP Power Hong Kong Limited in 2016, 34442 kWh of electricity were sold. (1 unit of electricity = 1 kWh)

The percentage of electricity consumed by each fuel type and their carbon emissions are as follows:

1. (a) The rate of carbon emissions is 2 kg/kWh. Explain this statement briefly in your own words.

For 1 kWh of electricity sold/consumed, 2 kg carbon dioxide emits to the air.

(b) Calculate the rate of carbon emissions in kg/kWh in the table above. Correct your answer to 2 decimal

### places.

(c) What do you notice about the rate of carbon emissions in kg/kWh of coal and natural gas?

1.0436 0.4182

= 2.4955

 2.50

 The carbon emissions of the electricity generated by coal is about 2.5 times more than that of natural gas.

(Calculation is not required. Students understand why natural gas was used to generate electricity as opposed to coal.)

The complete combustion of the carbon in the bag below would emit 0.54 kg of carbon dioxide to the air.

2. Assume that carbon emissions by nuclear power and hydro power are zero, calculate the average rate of carbon emissions per unit of electricity sold in kg/kWh in 2016. Correct your answer to 2 decimal places.

The carbon emissions per unit of electricity sold

=

6

6

## 

kg / kWh

= 18483.2

34442 kg / kWh

= 0.5366 kg / kWh

 0.54 kg / kWh

### Find the Average Daily Carbon Emissions from the Electricity Bill

The electric bill of the teacher was disclosed to the students.

The average daily electricity consumption was 9 units in March and 28 units in July in 2016. The maximum and minimum average daily carbon emissions attributed to his household were 15.12 kg and 4.86 kg respectively. Two bags of corresponding weights of carbon consumed in summer and winter were passed around. The students could experience the amount of carbon that was burnt to produce electricity for the daily consumption of the teacher. They were astonished to find the amount of carbon dioxide that was released into the atmosphere by each household every day.

3. According to the chart of average daily electricity consumption in your electricity bill of my house, calculate the maximum and minimum average daily carbon emissions attributed to your household in past years.

My electricity bill:

According to my electricity bill,

The maximum average daily carbon emission

= (28 × 0.54) kg

The minimum average daily carbon emission

= (9 × 0.54) kg

= 4.86 kg

4. Collect energy labels of different models of air conditioners. Investigate the carbon emissions of an 8-hour operation of the household air conditioners in summer night by the information on the energy labels of different air conditioners.

According to the energy label of an air conditioner, the determination energy consumption is based on 1200 hours/year operation.

Annual energy consumption = 966 kWh

If an air conditioner operates 8 hours per night in summer, the carbon emissions for a night

( 966 8 0.5366 1200  )kg  3.46 kg

A questionnaire was conducted after the tryout lesson. 89% of students agreed that they understood more about how the renewable energy sources help to reduce the amount of carbon dioxide in the air.